Spare tube: Sometimes, a tube is just too damaged to be patched, or has had a failure such as the valve stem breaking off which isn’t something that can be patched. To save weight and space, I usually keep a lightweight version of the right size tube for my bike. Since one of the first things I do with most bikes that I own is switch them over to heavy-duty thorn resistant tubes, I just take one of the originals and put that in the toolkit.
In addition to the Rema patches, put a new tire tube in your kit. The best method for dealing with a flat roadside is to swap out the tube and save the task of patching for later. If you’re not sure what size your tires are, it’s printed on the sidewall of the tire. This inner-tube buying guide has some photos of where to look. What brand is almost irrelevant as many tubes get manufactured in the same place, so whatever your local shop has behind the counter for under $10 will work fine. The only reason to spend more would be to save weight.
Basic first aid supplies: A few bandages of varying sizes. 6 Aspirin, or other OTC painkiller of choice. A few alcohol pads in sealed foil packs, useful for cleaning grease off grease and grit off of the bike, and also cleaning cuts on yourself if you take a spill. 1 day supply of any prescription drugs you need to take regularly. Wrap these up in tinfoil and tuck away. It might just save your day.
Whether you ride a single, 7, or 10 speed bike or anything in between, you will need a slightly different chain. The major difference is that they come in varying widths to accomodate the different spaces between the gears, but quality of construction is also a factor in choosing a chain. Inspecing the chain should be a part of your regular cycle maintenance procedure- It’s important to keep a chain well lubricated, but oil will also attract dirt and so different oils for specific riding conditions are available. Remember to clean your chain regularly to get the longest life out of it and the gears.